That's a good point when you talk about QBs who pull it down when necessary. That I agree with. Here's the three I listed and their stats so you can see what I was saying.......
Roger Staubach was called Roger the Dodger because of his scrambling ability. In 1971, he rushed for 343 yards — 2nd-most of any QB — with an 8.2 average and 2 touchdowns. He outrushed Bobby Douglass that year, and the Cowboys won the Super Bowl. Staubach ranked among the top 10 rushing QBs every full season of his career, and won two NFL titles.
Terry Bradshaw rushed for over 200 yards in six of his first seven seasons, a span that included two Super Bowl victories. In 1972, when the Steelers made the playoffs for the first time in team history, Bradshaw ran for a career-high 346 yards and 7 TDs, with a 6.0 average. When they won their first Super Bowl in '74, Bradshaw rushed for 224 yards in only 8 games, and out-rushed the entire Vikings team in Super Bowl IX (33-17). In 1975, Bradshaw was the 3rd-leading rusher among QBs, out-gained only by Bert Jones of the AFC East champion Colts, and by Staubach, whose Cowboys he met in Super Bowl X.
Steve Young was one of the most gifted runners ever to play quarterback in the NFL. He finished among the top three QBs in rushing yardage eight times, more than any other quarterback in history. He also led the NFL in passer rating six times, more than any other quarterback in history. His 43 rushing TDs are the most by any QB in the Super Bowl era, and his 96.8 passer rating is 2nd best all-time (Aaron Rodgers).